Physics

1

M. Dželalija, PhysicsCONTENTS Introduction

University of Molise, Valahia University of Targoviste, University of Split

Physics (lecture: 7 credits, laboratory: 0 credits)Mechanics (2 credits)Thermodynamics (1 credit)Electromagnetism (2 credits)Light and Optics (1 credit)Modern Physics (1 credit)

Literatures:R.A. Serway, J.S. Faughn, College Physics, Fifth Edition, Saunders College Publishing, 2000D. Haliday, R. Resnick, J. Walker, Fundamentals of Physics, Sixth Edition, John Wiley & Sons, 2001M. Dželalija, http://www.pmfst.hr/~mile/physics

Professor:Prof. Mile Dželalija, University of Split, CroatiaE-mail: [email protected]

Split, 2001.

M. Dželalija, PhysicsCONTENTS Mechanics

Physicsis concerned with the basic principles of the Universeis one of the foundations on which the other sciences are basedis tipical experimental scienceThe beauty of physics lies in the simplicity of its fundamental theoriesThe theories are usually expressed in mathematical form

Mechanicsis the first part of this lectureSometimes referred to as classical mechanics or Newtonian mechanicsis concerned with the effects of forces on material objectsThe first serious attempts to develop a theory of motion were made by Greek astronomers and philosophersA major development in the theory was provided by Isac Newton in 1687 when he published his PrincipiaToday, mechanics is of vital inportance to students from all disciplines

2

M. Dželalija, PhysicsCONTENTS The International System of Units

To report the result of a measurement of a certain physical quantity, a unit for the quantity must be defined.In 1960 an international committee agreed on a system of standards, called SI system.The SI units of length, mass, and time are the meter (m), kilogram (kg), and second (s)

The meter as the SI unit of length1799, defined as 1/10000000 of the distance from the Equator to the North Pole1983, redefined as the distance traveled by light in vacuum during a time interval of 1/299792458 second (this establishes that the speed of light is 299792458 m/s)

The kilogram as the SI unit of massdefinied as the mass of a specific platinum-iridium alloy cylinder

The second as the SI unit of timeBefore 1960, the second was defined as 1/86400 of average length of solar day in the year 1990.The second is now defined as 9192631700 times the period of oscilation of radiation from the cesium atom

M. Dželalija, PhysicsCONTENTS Examples

3

M. Dželalija, PhysicsCONTENTS Prefixes for SI Units

As a convinience when dealing with very large or very small measurements, we use the prefixes, which represents a certain power of 10, as a factor.Attaching a prefix to an SI unit has the effect of multiplying by the associated factor. For examples, we can express

a particular time interval as

a particular length as

a particular mass as

The most commonly used prefixes are:kilo, mega, and gigacenti, mili, micro, and nano

ns 2.35 s 1035.2 9 =⋅ −

km 7.2 m 102.7 3 =⋅

mg 5g 10105 kg 105 3-66 =⋅⋅=⋅ −

M. Dželalija, PhysicsCONTENTS Order-of-magnitude Calculations

We often need to change the units in which the physical quantity is expressed. We do so multiplying the original measurement by a conversion factor.

For example, to convert 2 min to seconds, we have

or, 15 in to centimeters (1 in = 2.54 cm)

Order-of-magnitude CalculationsSometimes it is useful to estimate an answer to a problem in which little information is given. This answer can then be used to determine whether or not a more precise calculation is necessery.When it is necessery to know a quantity only within a factor of 10, we refer to the order of magnitude of the quantity.For example,

the mass of a person might be 75 kg.We would say that the person’s mass is on the order of 10² kg.

s 120min

s 60min 2 min 2 =⋅=

cm 38.1in

cm 2.54in 15 in 15 =⋅=

4

M. Dželalija, PhysicsCONTENTS Examples .

The micrometer (1 μm) is often called the micron. How many microns make up 1 km?

31239333

2826232

734

km1008.1km101.1082)km 1037.6(14.334

34V

km101.5km106.509)km 1067.3(14.34R4Am104m10104km 40000km 637014.322

⋅≈⋅=⋅⋅⋅==

⋅≈⋅=⋅⋅⋅==⋅=⋅⋅=≈⋅⋅==

R

Rl

π

ππ

Earth is approximately a sphere of radius 6370 km. What are its circumference in meters, its surface area in square kilometers, its volume in cubic kilometers?

96-

3

10m 10m 10

m 1km 1

==μ

One gallon of paint (volume = 0.00378 m³) covers an area of 25 m². What is the thickness of the paint on the wall?

m 105.1m25

m 00378.0 42

3−⋅≈==

AVd

M. Dželalija, PhysicsCONTENTS Examples ..

Estimate the number of times your heart beats in a month. (Approximate time between normal hearbeat is 0.8 s)

910s3

s 36002436570s3y 70n ≈

⋅⋅⋅==

Estimate the number of breaths taken during an average life span of 70 years.

6103s0.8

s 360024301s0.8

month 1⋅≈

⋅⋅⋅==n

You can obtain a rough estimate of the size of a molecule by the following simple experiment. Let a droplet of oil spread out on a smooth water surface. The resulting oil slick will be approximately one molecule thick. Given an oil droplet of mass 0.9 mg and density 918 kg/m³ that spreads out into a circle of radius 41.8 cm on the water surface, what is the diameter of an oil molecule?

m107.1)m 418.0(kg/m 9183.14

kg 109 923

7

2

2

−−

⋅=⋅⋅

⋅==

==

rmd

drmV

πρ

πρ

5

M. Dželalija, PhysicsCONTENTS Motion in One Dimension

The part of mechanics that describes motion without regard to its causes is called kinematics.Here we will focus on one dimensional motion.

PositionTo describe the motion of an object, one must be able to specify its positionat all time using some convinient coordinate system.

For example, a particle might be located at x=+5 m, which means that it is 5 m in the positive direction from the origin. If it were at x=-5 m, it would be just as far from the origin but in the opposite direction.

Position is an example of a vector quantity, i.e. the physical quantity that requires the specification of both direction and magnitude. By contrast, a scalar is quantity that has magnitude and no direction.

DisplacementA change from one position to another position is called displacement

For examples, if the particles moves from +5 m to +12 m, then

The + sign indicates that the motion is in the positive direction. The plus sign for vector quantity need to be shown, but a minus sign must always be shown.

The displacement is a vector quantity.

12 xxx −=Δ1x 2x

m 7)m 5(m) 12( +=+−+=xΔ

M. Dželalija, PhysicsCONTENTS Average Velocity .

A compact way to describe position is with a graph of position plotted as a function of time.For example, an armadillo is first noticed when it is at the position –5 m. It moves toward x=0 m passes through that point at t=3 s , and then moves to increasingly larger positive values of x. Several quantities are associated with the phrase “how fast”. One of them is the average velocity which is the ratio of the displacement that occurs during a particular time interval to that interval:

A common unit of velocity is the meter per second (m/s).

12

12

ttxx

txv

−−

==ΔΔ

6

M. Dželalija, PhysicsCONTENTS Average Velocity ..

On a graph of versus , average velocity is the slope of the stright line that connects two particular positions. For the time interval 1 s to 4 s, the average velocity is ⟨v⟩=(+6 m)/(3 s)= +2 m/s.Like displacement average velocity has both magnitude and direction (it is another vector quantity).

Average speedis a different way of describing “how fast” a particle moves, and involves the total distance covered independent of direction:

is a scalar quantityFor the given example

x t

ts

Δdistance total

=

m/s 2s3m 6distance total

===t

sΔ

M. Dželalija, PhysicsCONTENTS Instantaneous Velocity

The instantaneous velocity is obtained from the average velocity by shrinking the time interval closer and closer to 0. As Δt dwindles, the average velocity ⟨v⟩approaches a limiting value, which is the velocity v at that instant:

For example, assume you have been observing a runner racing along a track, as given in one table. In another table there are calculated values of the time intervals. displacements, and average velocities. With some degree of confidence we can state that the instantaneous velocity of the runner was +2 m/s at the time 0.00 s.

The instantaneous speed, which is a scalar quantity, is defined as the magnitude of the instantaneous velocity.

txvv

tt ΔΔ

ΔΔ 00limlim→→

==

7


M. Dželalija, PhysicsCONTENTS Acceleration

When a particle’s velocity changes, the particle is said to accelerate. For motion along an axis, the average acceleration over a time interval is

where the particle has velocity at the time and then velocity at time The instantaneous acceleration (or simply acceleration) is defined as the limit of the average acceleration as the time interval goes to zero

Acceleration is vector quantity.The common unit of acceleration is the meter per second per second (m/s²).The acceleration at a certain time equals the slope of the velocity-time graph at that instant of time.

12

12

ttvv

tva

−−

==ΔΔ

1v 1t 2v 2t

tvaa

tt ΔΔ

ΔΔ 00limlim→→

==

8

M. Dželalija, PhysicsCONTENTS Constant Acceleration

In many types of motion, the acceleration is either constant or approximately so. In that case the instantaneous acceleration and average acceleration are equal

For convenience, let and be any arbitrary time Also, let (the initial velocity) and (the velocity at arbitrary time)With this notation we have

In a similar manner we can have

where is the position of the particle at initial time.Finally, from this two equations we can obtain expression that does not contain time

These equations may be used to solve any problem in one-dimensional motion with constant acceleration.

12

12

ttvvaa

−−

==

01 =t 2t t01 vv = vv =2

0x

atvv += 0

200 2

1 attvxx ++=

)(2 020

2 xxavv −+=

M. Dželalija, PhysicsCONTENTS Freely Falling Objects

All objects dropped near the surface of the Earth in the absence of air resistance fall toward the Earth with the same nearly constant acceleration.We denote the magnitude of free-fall accelerarion as g.The magnitude of free-fall acceleration decreases with increasing altitude. Furthemore, slight variations occur with latitude. At the surface of the Earth the magnitude is approximately 9.8 m/s². The vector is directed downward toward the center of the Earth.Free-fall acceleration is an important example of straight-line motion with constant acceleration.When air resistance is negligible, even a feather and an apple fall with the same acceleration, regardless of their masses.

9


At t=0, a particle moving along an x axis is at position –20 m. The signs of the particle’s initial velocity and constant acceleration are, respectively, for four situations: (a) +,+; (b) +,-; (c) -,+; (d) -,-.In which situation will the particle: (a) undergo a momentary stop, (b) definitely pass through the origin (given enough time), (c) definitely not pass through the origin?

200 2

1 attvxx ++=

(a) undergo a momentary stop: +,- and -,+.Initial velocity and constant acceleration must have opposite sign.

(b) definitely pass through the origin (given enough time): +,+ and -,+. Constant acceleration and initial position must have opposite sign.

(c) definitely not pass through the origin: -,-.Constant acceleration and initial position must have the same sign, and initial velocity must not have opposite sign with high magnitude.

atvv += 0


10

M. Dželalija, PhysicsCONTENTS Examples …

M. Dželalija, PhysicsCONTENTS Examples ….

11

M. Dželalija, PhysicsCONTENTS Examples …..

M. Dželalija, PhysicsCONTENTS Two-Dimensional Motion

12

M. Dželalija, PhysicsCONTENTS Projectile Motion .

M. Dželalija, PhysicsCONTENTS Projectile Motion ..

13


M. Dželalija, PhysicsCONTENTS Exercises .

14

M. Dželalija, PhysicsCONTENTS Exercises ..

M. Dželalija, PhysicsCONTENTS Exercises …

1

M. Dželalija, PhysicsCONTENTS The Concept of Force

Classical mechanics describes the relationship between the motion of an object and the force acting on it. There are conditions under which classical mechanics does not apply. Most often these conditions are encountered when dealing with objects whose size is comparable to that of atoms or smaller and/or which move at speed of light.

If the speeds of the interacting objects are very large, we must replace Classical mechanics with Einstein’s special theory of relativity, which hold at any speed, including those near the speed of light.If the interacting bodies are on the scale of atomic structure, we must replace Classical mechanics with quantum mechanics.Classical mechanics is a special case of these two more comprehensive theories. But, still it is a very important special case because it applies to the motion of objects ranging in size from the very small to astronomical.

The concept of forceForce is an interaction that can cause deformation and/or change of motion of an objectForce is a vector quantityFundamental forces are:

gravitationalelectromagneticweak nuclearstrong nuclear

M. Dželalija, PhysicsCONTENTS Newton’s First Law

Before Newton formulated his mechanics, it was thought that some influence was needed to keep a body moving at constant velocity. A body was thought to be in its “natural state” when it was at rest.Galileo was the first to take a different approach. He concluded that it is not the nature of an object to stop once set in motion. This approach to motion was later formalized by Newton in a form that has come to be known as Newton’s first law of motion: “An object at rest remains at rest, and an object in motion continues in motion

with constant velocity, unless it experiences a net external force.”Newton’s first law says that when the net external force on an object is zero, its acceleration is zero.

Inertial Reference FramesNewton’s first law is not true in all reference frames, but we can always find reference frames in which it is true. Such frames are called inertial reference frames, or simply inertial frames.A inertial reference frame is one in which Newton’s laws hold.Other frames are noninertial frames. Isaac Newton

2

M. Dželalija, PhysicsCONTENTS Mass and Inertia

The tendency of an object to resist any attempt to change its motion is called the inertia of the object.Mass is a measurement of inertia.The greater the mass of a body, the less it accelerates under the action of an applied force.Mass is a scalar quantity that obeys the rules of ordinary arithmetic.Mass is an intrinsic characteristic of a body – that is a characteristic that automatically comes with the existance of the body. It has no definition. The mass of a body is the characteristic that relates a force on the body to the resulting acceleration.The SI unit of mass is the kilogram (1 kg).For example, if a given force acting on a 3-kg mass produces an acceleration of 4m/s², the same force applied to a 6-kg mass will produce an acceleration of only 2 m/s².Inertia is the principle that underlies the operation of seat belts and air begs.

M. Dželalija, PhysicsCONTENTS Newton’s Second Law

Newton’s first law explains what happens to an object when the net force acting on it is zero. Newton’s second law answers the question of what happens to an object that has nonzero force acting on it.From observations, we can conclude that the acceleration of an object is directly proportional to the net force acting on it, and these observation are summarized in Newton’s second law:“The net force on a body is equal to the product of the body’s mass and the

acceleration of the body.”In equation form:

where represents the vector sum of all external forces acting on the object, is its mass, and is the acceleration of the object.This equation is a vector equation, and it is equivalent to three component equations:

The SI unit of force is the newton (1 N = 1 kgm/s²).

zzyyxx maFmaFmaF === ∑∑∑

∑ Fr

m ar

amF rr=∑

3

M. Dželalija, PhysicsCONTENTS Some Particular Forces .

The Gravitational Force and WeightThe force exerted by the Earth on an object is the gravitational forceThis force is directed approximately toward the center of the Earth and its magnitude varies with location.The magnitude of the gravitational force is called the weight of the object

where g is the magnitude of the free-fall acceleration.Weight is not an inherent property of an object.

The Normal ForceIf you stand on a mattress, Earth pulls you downward, but you are stationary. The reason is that the mattress, because it deformes, pushes up on you. This force from the mattress is called a normal forceThe normal force is perpendicular to the surface.

gFr

mgFW g ==

NFr

M. Dželalija, PhysicsCONTENTS Some Particular Forces ..

The Frictional ForceIf we slide or attempt to slide a body over a surface, the motion is resisted by a bonding between the body and the surface. The resistence isconsidered to be a single force called the frictional forceThis force is very important in our everyday lives. They allow us to walk or run and are necessery for the motion of wheeled vehicles.The frictional force is directed along the surface, opposite the direction of the intended motion.For an object in motion the frictional force we call kinetic frictional force; otherwise static frictional force.Both, kinetic and static frictional force are proportional to the normal force acting on the object

where are coefficients of staticand kinetic friction.

fFr

NkkfNssf FFFF μμ == ,max,,

ks μμ ,

4

M. Dželalija, PhysicsCONTENTS Some Particular Forces ...

The Tension ForceWhen a cord is attached to a object and pulled taut, the cord pulls on the object with the force called a tension force.The force is directed away from the object and along the cord.

The Spring ForceA good approximation for many springs, the force from a spring is proportional to the displacement of the free end from its position when the spring is in the relaxed state

This is known as Hooke’s law.The minus sign indicates that the spring force is always opposite in direction from the displacement of the free end.The constant k is called the spring constant

It is a measure of the stiffness of the spring. The larger k is, the stiffer the spring.

Note that a spring force is a variable force.

TFr

TFr

Fr

dr

dkFrr

−=

M. Dželalija, PhysicsCONTENTS Newton’s Third Law

A force is exerted on an object when that object comes into contact with some other object.Newton recognized that forces in nature always exist in pair. He described this type of situation in terms of his third law of motion:“When two objects interact, the force on the object from each other are always

equal in magnitude and opposite in direction.”

For example, the force acting on a freely falling projectile is the force of the Earth on the projectile, and the magnitude of this force is mg. The reaction to this force is the force of the projectile on the Earth. The reaction force must accelerate the Earth toward the projectile. However, because the Earth has such a large mass, its acceleration due to this reaction force is negligibly small.

5



TFr

gFr

NFr

6

M. Dželalija, PhysicsCONTENTS Examples ...


An object has only one force acting on it. Can it be at rest? Can it have an acceleration?If a single force acts on it, the object must accelerate. If an object accelerates,

at least one force must act on it.

An object has zero acceleration. Does this mean that no forces act on it?If an object has no acceleration, you cannot conclude that no forces act on it.

In this case, you can only say that the net force on the object is zero.

Is it possible for an object to move if no net force acts on it?Motion can occur in the absence of a net force. Newton’s first law holds that an

object will continue to move with a constant speed and in a straight line if there is no net force acting on it.

What force causes an automobile to move?The force causing an automobile to move is the force of friction between the

tires and the roadway as the automobile attempts to push the roadway backward.

7


What force causes a propeller airplane to move?The force driving a propeller airplane forward is the reaction force of the air on

the propeller as the rotating propeler pushes the air backword.

What force causes a rowboat to move?In a rowboat, the rower pushes the water backword with the oars. The water

pushes forward on the oars and hence the boat.

In a tug-of-war between two athletes, each pulls on the rope with a force of 200 N. What is the tension in the rope?The tension in the rope is the maximum force that occurs in both directions. In

this case, then, because both are pulling with a force of 200 N, the tension is 200 N.

Identify the action-reaction pairs in the following situations: a man takes a step; a gust of wind strikes a window.As a man takes a step, the action is the force his foot exerts on the Earth; the

reaction is the force of the Earth on his foot. As a gust of wind strikes a window, the action is the force exerted on the window by the air molecules; the reaction is the force on the air molecules exerted by the window.

M. Dželalija, PhysicsCONTENTS Exercises ...

Suppose you are driving a car at a high speed. Why you should you avoid alamming on your brakes when you want to stop in the shortest possible distance?The brakes may lock and the car will slide farther than it would if the wheels

continued to roll because the coefficient of kinetic friction is less than the coefficient of static friction. Hence, the force of kinetic friction is less than the maximum force of static friction.

An object has a mass of 6 kg and acceleration of 2 m/s². What is the magnitude of the resulting force acting on it?

The force of the wind on the sails of a sailboat is 390 N north. The water exerts force of 180 N east. If the boat has a mass of 270 kg, what are the magnitude and direction of its acceleration?

N 12)s/2(kg) 6( 2 =⋅== maF

8

M. Dželalija, PhysicsCONTENTS Exercises ....

M. Dželalija, PhysicsCONTENTS Exercises .....

A house is bilt on the top of a hill with a nearby 45° slope. An engineering study indicates that the slope angle should be reduced because the top layers of soil along the slope might slip past the lower layers. If the static coeficcient of friction between two such layers is 0.5, what is the least angle φ through which the present slope should be reduced to prevent slipping?(A: φ > 18.4°)

0

0

0

4.1845

6.26arctan

tancossin

=−=

==

=

=

θφ

μθ

θθθμ

mgmg

1

M. Dželalija, PhysicsCONTENTS Work .

The concept of energy is one of the most important in the world of science. In everyday use, the term energy has to do with the cost of fuel for transportation and heating, electricity for lights and appliances, and the foods we consume.

Energy is present in the Universe in a variety of forms, including mechanical energy, chemical energy, electromagnetic energy, nuclear energy, and many others.

Here we are concerned only with mechanical energy, and begin by defining work.Work

M. Dželalija, PhysicsCONTENTS Work ..

As an example of the distinction between this definition of work and our everyday understanding of the word, consider holding a heavy book atarm’s length. After 5 minutes, your tired arms may lead yout to think that you have done a considerable amout of work. According to our definition, however, you have done no work on the book. Your muscles are continuosly contracting and relaxing while the book is beingsupported. Thus, work is being done on your body, but not on the book.A force does no work on a object if the object does not move.The sign of the work depends on the angle θ between the force and displacement.Work is a scalar quantity, and its units is joule (1 J = 1 Nm)For example, a man cleaning his apartment pulls the canister of a vacuum cleaner with a force of magnitude 50 N at an angle 30°. He moves the vacuum cleaner a distance of 3 m. Calculate the work done by the force.

J130)m 3)(30 )(cosN 50( cos 0

=== dFW θ

2

M. Dželalija, PhysicsCONTENTS Kinetic energy

M. Dželalija, PhysicsCONTENTS Example

3

M. Dželalija, PhysicsCONTENTS Gravitational potential energy

M. Dželalija, PhysicsCONTENTS Conservative and nonconservative forces

Conservative forcesA force is conservative if the work it does on an object moving between two points is independent of the path the object takes between the points. In other words, the work done on an object by a conservative force depends only on the initial and final positions of the object.The gravitational force is conservativ.

Nonconservative forcesA force is nonconservative if it leads to a dissipation of mechancal energy.If you moved an object on a horizontal surface, returning it to the same location and same state of motion, but found it necessary to do net work on the object, then something must have dissipated the energy transferred to the object. That dissipative force is recognized as friction between object and surface.Friction force is a nonconservative force.

4

M. Dželalija, PhysicsCONTENTS Conservation of mechanical energy

Conservative principles play a very important role in physics, and conservation of energy is one of the most important.Let us assume that the only force doing work on the system is conservative. In this case we have

or

The total mechanical energy in any isolated system of objects remains constant if the objects interact only through conservative forces.This is equivalent to saying that, if the kineic energy of a conservative system increases by some amount, the potential energy of the system must decrease by the some amount.If the gravitational force is the only force doing work on an object, then the total mechanical energy of the object remains constant

1221 kkpp EEEEW −=−=

2211 pkpk EEEE +=+

2221

21 2

121 mghmvmghmv +=+


5

M. Dželalija, PhysicsCONTENTS Elastic potential energy

The concept of potential energy is of tremendous value in descriptions of certain types of mechanical energy. One of these is the motion of a mass attrached to a streched or compressed spring.In order to compress the spring, we must exert on the block a force of

where k is a constant for a particular spring called the spring constant.

The force increases linearly with position.It is possible to find the work done by the applied force. This work is stored in the compressed spring as elastic potential energy

The elastic potential energy stored in the spring is zero when the spring is in equilibrium (x=0).Note that energy is stored in the spring when it is streched as well.

xkF rr−=

2, 2

1 kxE ep =

M. Dželalija, PhysicsCONTENTS Work and nonconservative forces

6

M. Dželalija, PhysicsCONTENTS Power


7



8

M. Dželalija, PhysicsCONTENTS Exercises ….

1

M. Dželalija, PhysicsCONTENTS Center of Mass

M. Dželalija, PhysicsCONTENTS Example .

2

M. Dželalija, PhysicsCONTENTS Example ..

M. Dželalija, PhysicsCONTENTS Linear Momentum

3


M. Dželalija, PhysicsCONTENTS Impulse

4

M. Dželalija, PhysicsCONTENTS Linear Momentum of a System of Particle

M. Dželalija, PhysicsCONTENTS Newton’s Second Law

5


M. Dželalija, PhysicsCONTENTS Conservation of Linear Momentum

6

M. Dželalija, PhysicsCONTENTS Collisions

M. Dželalija, PhysicsCONTENTS Type of Collision

7

M. Dželalija, PhysicsCONTENTS Example .

M. Dželalija, PhysicsCONTENTS Example ..

8

M. Dželalija, PhysicsCONTENTS Example ...

1

M. Dželalija, PhysicsCONTENTS Angular Position


2

M. Dželalija, PhysicsCONTENTS Angular Velocity

M. Dželalija, PhysicsCONTENTS Angular Acceleration

3

M. Dželalija, PhysicsCONTENTS Rotation with Constant Angular Acceleration

M. Dželalija, PhysicsCONTENTS Relations between Angular and Linear Quantities

4


M. Dželalija, PhysicsCONTENTS Torque

5

M. Dželalija, PhysicsCONTENTS Moment of Inertia

M. Dželalija, PhysicsCONTENTS Newton’s Second Law for Rotation

6

M. Dželalija, PhysicsCONTENTS Conservation of Angular Momentum

M. Dželalija, PhysicsCONTENTS Rotational Kinetic Energy

7

M. Dželalija, PhysicsCONTENTS Centripetal Forces

M. Dželalija, PhysicsCONTENTS Newton’s Universal Law of Gravitation

8


An object executes circular motion with a constant speed whenever a net force of constant magnitude acts perpendicular to the velocity. What happens to the speed if the force is not perpendicular to the velocity?

An object can move in a circle even if the total force on it is not perpendicular to its velocity, but then its speed will change. Resolve the total force into an inward radial component and a tangential component. If the tangential force is forward, the object will speed up, and if the tangential force acts backward, it will slow down.

An object moves in a circular path with constant speed. Is the object’s velocity constant? Is its acceleration constant? Explain.

As an object moves in its circular path with constant speed, the direction of the velocity vector changes. Thus, the velocity of the object is not constant. The magnitude of its acceleration remains constant, and is equal to v²/r.The acceleration vector is always directed toward the center of the circular path.

1

M. Dželalija, PhysicsCONTENTS States of Matter

M. Dželalija, PhysicsCONTENTS Solids

2

M. Dželalija, PhysicsCONTENTS Deformation of Solids

M. Dželalija, PhysicsCONTENTS Elasticity in Length

3

M. Dželalija, PhysicsCONTENTS Elasticity of Shape

M. Dželalija, PhysicsCONTENTS Volume Elasticity

4

M. Dželalija, PhysicsCONTENTS Density and Pressure

M. Dželalija, PhysicsCONTENTS Pressure with Depth

5

M. Dželalija, PhysicsCONTENTS Archimedes’s Principle and Bouyant Forces

M. Dželalija, PhysicsCONTENTS Fluids in Motion

6

M. Dželalija, PhysicsCONTENTS Equation of Continuity

M. Dželalija, PhysicsCONTENTS Bernoulli’s Equation

7



8



1

M. Dželalija, Physics (Part 7)CONTENTS Simple Harmonic Motion

M. Dželalija, Physics (Part 7)CONTENTS Elastic Potential Energy

2

M. Dželalija, Physics (Part 7)CONTENTS Speed as a Function of Position

M. Dželalija, Physics (Part 7)CONTENTS Period and Frequency

3

M. Dželalija, Physics (Part 7)CONTENTS Position as a Function of Time

M. Dželalija, Physics (Part 7)CONTENTS Motion of a Pendulum .

4

M. Dželalija, Physics (Part 7)CONTENTS Motion of a Pendulum ..

M. Dželalija, Physics (Part 7)CONTENTS Damped Oscillations

5

M. Dželalija, Physics (Part 7)CONTENTS Resonance

We learned that the energy of a damped oscillator decreases in time because of friction. It is possible to compensate for this energy loss by applying an external force that does positive work on the system.

For example, suppose a mass-spring system, having some natural frequency of vibration, is pushed back and forth with a periodic force whose frequency is f. The system vibrates at the frequency of the driving force. This type of motion is referred to as a forced vibration. Its amplitude reaches a maximum when the frequency of the driving force equals the natural frequency of the system, called the resonant frequency of the system. Under this condition, the system is said to be in resonance.

Resonance vibrations occur in a wide variety of circumstances, as you can see on the figures.

M. Dželalija, Physics (Part 7)CONTENTS Wave Motion

There are a wide variety of physical phenomena that have wave-like characteristics. The world is full of waves: sound waves, waves on strings, earthquake waves, electromagnetic waves. All of these waves have as their source a vibrating object.

Thus, we shall use the terminology and concepts of simple harmonic motion as we move into the study of wave motion. In the case of sound waves, the vibrations that produce waves arise from such source as a person's vocal cords or a plucked guitar string. The vibrations of electrons in an antenna produce radio or television waves.

For example, when we observe a water wave, what we see is a rearrangement of the water's surface. Without the water there would be no wave. A wave travelling on a string would not exist without the string. Sound waves travel through air as a result of pressure variations from point to point. Therefore, we can consider a wave to be the motion of a disturbance. (We will discuss later electromanetic waves which do not require a medium)

Mechanical waves require: a source of disturbance, a medium that can be disturbed, and physical mechanism through which adjacent portions of the medium can influence each other.

All waves carry energy and momentum.

6

M. Dželalija, Physics (Part 7)CONTENTS Types of Waves

One of the simplest ways to demonstrate wave motion is to flip one end of a long rope that is under tension. The bump (called a pulse) travels to thr right with a definite speed. A disturbance of this type is called a traveling wave.

As a pulse travels along the rope, each segment of the rope that is disturbed moves perpendicularly to the wave motion. A travelling wave such as this is called a transverse wave.

In another class of waves, called longitudinal waves, the particles of the medium undergo displacements parallel to the direction of wave motion. Sound waves in air, for instance, are longitudinal. Their disturbence corresponds to a series of high- and low-pressure regions that may travel through air or through any material with a certain speed.

M. Dželalija, Physics (Part 7)CONTENTS Wavelength

7

M. Dželalija, Physics (Part 7)CONTENTS Waves on Strings

M. Dželalija, Physics (Part 7)CONTENTS Interference of Waves

Many interesting wave phenomena in nature are impossible to describe with a single moving wave. Instead, one must analyze what happens when two or more waves pass through the same region of space. For such analyses one can use the superposition principle: if two or more traveling waves are moving through a medium, the resultant wave is found by adding together the displacement of the individual waves point by point.

One consequence of the superposition principle is that two traveling waves can pass through each other without being destroyed or even altered.

If two waves having the same frequency and amplitude are in phase, the resultant wave when they combine has the same frequency as the individual waves but twice their amplitude. Waves coming together like this are said to be in phase and to undergo constructive interference.

When two waves with the same frequency and amplitude are inverted (180° out of phase) one to the other, the result when they combine is complete cancellation. Waves undergo destructive interference.

8

M. Dželalija, Physics (Part 7)CONTENTS Reflection of Waves

Whenever a traveling wave reaches a boundary, part or all of the wave is reflected. For example, consider a pulse traveling on a string that is fixed at one end. When the pulse reaches the wall, it is reflected. Note, that the reflected pulse is inverted (according to Newtons’s third law).

In a case in which the pulse arrives at the string’s end, which is attached to a ring of negligible mass that is free. Pulse is reflected, but it is not inverted.

M. Dželalija, Physics (Part 7)CONTENTS Exercises .

9

M. Dželalija, Physics (Part 7)CONTENTS Exercises ..

M. Dželalija, Physics (Part 7)CONTENTS Exercises ...

10

M. Dželalija, Physics (Part 7)CONTENTS Exercises ....

M. Dželalija, Physics (Part 7)CONTENTS Exercises ,

11

M. Dželalija, Physics (Part 7)CONTENTS Exercises ,.

M. Dželalija, Physics (Part 7)CONTENTS Exercises ,..

1

M. Dželalija, PhysicsCONTENTS Producing a Sound Wave

Sound waves are the most important example of longitudinal waves. Any sound wave has its source in a vibrating object. Musical instruments produce sounds in a variety of ways. For example, the sound from a clarinet is produced by a vibrating reed, the sound from a piano by a vibrating strings, and the sound from a singer by vibrating vocal folds.

Sound waves are longitudinal waves traveling through a medium, such as air. In order to investigate how sound waves are produced, we focus our attention on the tuning fork, a common device for producing pure musical notes. A tuning fork consists of two metal prongs that vibrate when struck. Their vibration disturbs the air near them.

A region of high molecular density and high air pressure is called a compression. A region of lower than normal density is called a rarefaction. As the tuning fork vibrates, a series of condensations and rarefactions moves outward, away from the fork. The crests of the wave correspond to condensations, and the troughs to rarefactions.

M. Dželalija, PhysicsCONTENTS Characteristics of Sound Waves

General motion of air molecules near a vibrating object is back and forth between regions of compression and rarefaction. Back-and-forth molecular motion in the direction of the disturbance is characteristic of a longitudinal wave.

Sound waves fall into three categories covering different ranges of frequencies.

Audiable waves are longitudinal waves that lie within the range of sensitivity of the human ear, approximately 20 Hz to 20000 Hz.

Infrasonic waves are longitudinal waves with frequencies below the audible range. Earthquarke waves are an example.

Ultrasonic waves are longitudinal waves with frequencies above the audible range for humans. For example, certain types of whistlesproduce ultrasonic waves. Some animals, such as dogs, can hear the waves emitted by these whistles, even though humans cannot.

2

M. Dželalija, PhysicsCONTENTS Speed of Sound

M. Dželalija, PhysicsCONTENTS Energy and Intensity of Sound Waves

3

M. Dželalija, PhysicsCONTENTS Intensity Levels in Decibels

M. Dželalija, PhysicsCONTENTS Courves of Intensity Level

Figure shows the frequency response curves of an average human ear for sounds of equal loudness, ranging from 0 to 120 dB. To interpret this series of graphs, take the bottom curve as the threshold of hearing. The easiest frequencies to hear are around 3300 Hz.

4

M. Dželalija, PhysicsCONTENTS The Doppler Effect

M. Dželalija, PhysicsCONTENTS Shock Waves

Shock waves are produced when the source speed exceeds the wave velocity. Figure describes this situation graphically. The circles represent spherical wavefronts emitted by the source at various times during its motion. The conical wavefront produced is known as a shock wave.

A shock wave carries a great deal of energy concentrated on the surface of the cone, with the great pressure variations. Shock waves are unplesent to hear and can damage buildings when, for example, aircraft fly supersonically at low altitudes.

5

M. Dželalija, PhysicsCONTENTS Standing Waves .

M. Dželalija, PhysicsCONTENTS Standing Waves ..

6



7

M. Dželalija, PhysicsCONTENTS Exercises …

M. Dželalija, PhysicsCONTENTS Exercises ….

8

M. Dželalija, PhysicsCONTENTS Exercises …..

1

M. Dželalija, PhysicsCONTENTS Temperature

We now move to a new branch of physics, thermal physics. We shall find that quantitative descriptions of thermal phenomena require careful definitions of the concepts of temperature, heat, and internal energy.

In order to understant the concept of temperature, it is useful to define thermal contact and thermal equilibrium.

Two objects are in thermal contact with each other if energy can be exchanged between them. Thermal equilibrium is the situation in which two objects in thermal contact with each other case to have any exchange of energy.

Zeroth law of thermodynamics: If bodies A and B are separately in thermal equilibrium with a third body, C, then A and B will be in thermal equilibrium with each other if placed in thermal contact.

This statement, insignificant and obvious as it may seem, is easily proved experimentally and is very important because it makes it possible to define temperature. We can think of temperature as the property that determines whether or not an object will be in thermal equilibrium with other objects. Two objects in thermal equilibrium with each other are at the same temperature.

M. Dželalija, PhysicsCONTENTS Thermometers and Temperature Scales

Thermometers are devices used to measure the temperature of a system. All thermometers make use of a change in some physicalproperty with temperature. One common thermometer ineveryday use consists of a mass of liquid (usually mercuryor alchocol) that expands into a glass capillary tube when heated. In this case the physical property is the change involume of a liquid. The thermometer can be calibrated byplacing it in thermal contact with some natural systems (E.g. mixture water and ice). It is defined to have a temperature of zero degrees Celsius (0°C). Another commonly used system is a mixture of water and steam at atmospheric pressure (100°C).

In a gas thermometer, the temperature readings are nearly independent of the type of gas used, so long as the gas pressure is low and the temperature is well above the point at which the gas liquifies. If the curves in Figure are extended back toward negative temperatures, in every case the pressure is zero when the temperature is -273.15°C. This significant temperature is used as the basis for the Kelvin scale, which sets –273.15°C as its zero point (0 K). The size of a kelvin is identicalto the size of a degree on the Celsius scale: T(K) = T(°C) + 273.15

2

M. Dželalija, PhysicsCONTENTS Thermal Expansion of Solids and Liquids .

M. Dželalija, PhysicsCONTENTS Thermal Expansion of Solids and Liquids ..

3

M. Dželalija, PhysicsCONTENTS An Example

When the temperatures of a brass rod and a steel rod of equal length are raised by the same amount from some common initial value, the brass rod expands more than the steel rod because brass has a larger coefficient of expansion than steel. A simple device that utilizes this principle, called a bimetallic strip, is found in practical devices such as thermostats. The strip is made by securely bonding two different metals together. As the temperature of the strip increases, the two metals expand by different amounts and the strip bends, as in figure.

M. Dželalija, PhysicsCONTENTS The Unusual Behavior of Water

Liquids generally increase in volume with increasing temperature and have volume expansion coefficients about ten times greater than those of solids. Water is an exception to this rule, as we can see from its density-versus-temperature curve. As the temperature increases from 0°C to 4°C, water contracts and thus its density increases. Above 4°C, water expands with increasing temperature. The density of water reaches its maximum value 4 degrees above the freezing point.

When the atmospheric temperature is between 4°C and 0°C the surface water expands as it cools, becoming less dense than the water below it. The mixing process stops, and eventually the surface water freezes. As the water freezes, the ice remains on the surface because ice is less dense than water. The ice continues to build up on the surface, and water near the bottom of the pool remains at 4°C. If this did not happen, fish and other forms of marine life would not survive.

4

M. Dželalija, PhysicsCONTENTS Macroscopic Description of an Ideal Gas

M. Dželalija, PhysicsCONTENTS Molecular Interpretation of Pressure .

We discusses the properties of an ideal gas, using such quantities as pressure, volume, number of moles, and temperature. We shall find that pressure and temperature can be understood on the basis of what is happening on the atomic scale. We use the kinetic theory of gases to show that the pressure a gas exerts on the walls of its container is a consequance of the collisions of the gas molecules with the walls.

We make the following assumptions of molecular model for an ideal gas: The number of molecules is large, and the average separation between them is large compared with their dimensions. This means that the molecules occupy a negligible volume in the container. The molecules obey Newton's laws of motion, but as a whole they move randomly. Any molecule can move equally in any direction. The molecules undergo elastic collisions with each other and with the walls of the container. Thus, in the collisions kinetic energy is constant. The forces between molecules are negligible except during a collision. The gas under consideration is a pure substance. That is, all molecules are identical.

5

M. Dželalija, PhysicsCONTENTS Molecular Interpretation of Pressure ..

M. Dželalija, PhysicsCONTENTS Molecular Interpretation of Temperature

6



7



8


M. Dželalija, PhysicsCONTENTS Exercises ,.

9

M. Dželalija, PhysicsCONTENTS HomeLab

Tie and tape two inverted empty paper bags to the ends of a rod as in the figure. Balance the setup. Then place a candile under one of the bags and note what happens. Why does this system become unbalanced? What do your results tell you concerning the density of warm air versus the density of cold air?

1

M. Dželalija, PhysicsCONTENTS Heat

M. Dželalija, PhysicsCONTENTS Specific Heat

2

M. Dželalija, PhysicsCONTENTS Sea Breezes

The fact that the specific heat of water is higher than that of land is responsible for the pattern of air flow at a beach. During the day, the Sun adds roughly equal amounts of energy to beach and water, but the lower specific heat of sand causes the beach to reach a higher temperature than the water. As a consequence, the air above the land reaches a higher temperature than that over the water, and cooler air from above the water is drawn in to displace this rising hot air, resulting in a breeze from water to land during the day. Because the hot air gradually cools as it rises, it subsequently sinks, setting up the circulating pattern shown in figure. During the night, the land cools more quickly than the water, and the circulating pattern reverses itself because the hotter air is now over the water. The offshore and onshore breezes are certainly well known to sailors.

A similar effect produces rising layers of air, called thermals, that can help eagles to soar higher and hang gliders to stay in flight longer.

M. Dželalija, PhysicsCONTENTS Conservation of Energy: Calorimetry

3

M. Dželalija, PhysicsCONTENTS Latent Heat and Phase Changes

M. Dželalija, PhysicsCONTENTS Table: Latent Heat

Latent heat of fusion and vaporization

4

M. Dželalija, PhysicsCONTENTS Example (Water) .

M. Dželalija, PhysicsCONTENTS Example (Water) ..

5

M. Dželalija, PhysicsCONTENTS Description of Phase Changes

Phase changes can be described in terms of rearrangements of molecules when heat is added to or removed from a substance. Consider first the liquid-gas phase change. The molecules in a liquid are close together, and the forces between them are stronger than those between the more widely separated molecules of a gas. Therefore, work must be done on the liquid against these attractive molecular forces in order to separate the molecules. The latent heat of vaporization is the amount of energy that must be added to the liquid to accomplish this.

Similarly, at the melting point of a solid, we imagine that the amplitude of vibration of the atoms about their equilibrium positions becomes great enough to allow the atoms to pass the barriers of adjacent atoms and move to their new positions. The new locations are, on the average, less symmetrical and therefore have higher energy. The latent heat of fusion is equal to the work required at the molecular level to transform the mass from the ordered solid phase to the disordered liquid phase.

The average distance between atoms is much greater in the gas phase than in either the liquid or the solid phase. Each atoms or molecule is removed from its neighbors, without the compensation of attractive forces to new neighbors. Therefore, it is not surprising that more work is required at the molecular level to vaporize a given mass of substance than to melt it. Thus the latent heat of vaporization is much greater than the latent heat of fusion (see Table: Latent Heat).

M. Dželalija, PhysicsCONTENTS Heat Transfer by Conduction

There are three ways in which heat energy can be transferred from one location to another: conduction, convection, and radiation. Regardless of the process, however, no net heat transfer takes place between a system and its surroundings when the two are at the same temperature.

Each of the methods of heat transfer can be examined by considering the ways in which you can warm your hands over an open fire. If you insert a copper rod into flame, the temperature of the metal in your hand increases rapidly. Conduction, the process by which heat is transferred from the flame through the copper rod to your hand, can be understood by examining what is happening to the atoms of the metal. As the flame heats the rod, the copper atoms near the flame begin to vibrate with greater and greater amplitudes. These vibrating atoms collide with their neighbors and transfer some of their energy in the collisions.

The rate of heat conduction depends on the properties of the substance being heated. Metals are good conductors of heat because they contain large numbers of electrons that are relatively free to move through the metal and transport energy from one region to another. In these conductors heat conduction takes place both via the vibration of atoms and via the motions of free electrons.

6

M. Dželalija, PhysicsCONTENTS Heat Transfer Rate

M. Dželalija, PhysicsCONTENTS Heat Transfer by Convection

The air directly above the flame is heated and expands. As a result, the density of the air decreases and the air rises. This warmed mass of air heats your hands as it flows by. Heat transferred by the movement of a heated substance is said to have been transferred by convection. When the movement results from differences in density, as it does in air around a fire, it is referred to as natural convection. When the heated substance is forced to move by a fan or pump, as in some heating systems, the process is called forced convection.

The circulating pattern of air flow at a beach is an example of convection. Convection process occurs when a room is heated by a radiator. The warm air expands and rises to the ceiling because of its lower density. The denser regions of cooler air from above replace the warm air. Your automobile engine is maintained at a safe operating temperature by a combination of conduction and forced convection.

7

M. Dželalija, PhysicsCONTENTS Example: Algal Blooms

The algal blooms often seen in temperate lakes and ponds during spring or autumn are caused by convection currents in the water. During the summer, bodies of water develop temperature gradients such that an upper warm layer of water is separated from a lower cold layer by a buffer zone called a thermocline. In the spring or autumn, the temperatures changes in the water break down this thermocline, setting up convection currents that mix the water. This mixing process transports nutrients from the bottom to the surface. The nutrient-rich water forming at the surface can cause a rapid, temporary increase in the population of algae.

M. Dželalija, PhysicsCONTENTS Heat Transfer by Radiation

The third way of transferring heat is through radiation. You have must likely experienced radiant heat when sitting in front of a fireplace. The hands that are placed to one side of the flame are not in physical contact with flame, and therefore conduction cannot account for the heat transfer. Furthermore, convection is not important in this situation because the hands are not above the flame in the path of convection currents. The important process in this case is the radiation of heat energy.

All objects continuously radiate energy in the form of electromegnetic waves, which we shall discuss later. Electomagnetic radiation associated with the loss of heat energy from an object at a temperature of a few hundred kelvins is referred to as infrared radiation.

The surface of the Sun is at a few thousand kelvins and most strongly radiates visible light. Approximately 1340 J of sunlight energy strikes 1 m² of the top of the Earth’s atmosphere every second. Some of this energy is reflected back into space, and some is absorbed by the atmosphere, but enough arrives at the surface of the Earth.

8

M. Dželalija, PhysicsCONTENTS Stefan’s Law

M. Dželalija, PhysicsCONTENTS Global Warming and Greenhouse Gases

During the day, sunlight passes into the greenhouse and is absorbed by the walls, earth, and plants. This absorbed visible light is subsequently re-radiated as infrared radiation, which causes the temperature of the interior to rise. In addition, convection currents are inhibited in a greenhouse.

A phenomenon known as the greenhouse effect can also play a major role in determining the Earth’s temperature. Earth’s atmosphere is a good transmitter of visible radiation and a good absorber of infrared radiation. Carbon dioxide in the Earth’s atmosphere allows incoming visible radiation from the Sun to pass through more easily than infrared radiation. The visible light that reaches the Earth’s surface is absorbed and re-radiated as infrared light, which in turn is absorbed by the Earth’s atmosphere.

At present, about 350 billions tons of carbon dioxide are released into the atmosphere each year. Most of this gas results from human activities such as the burning of fosil fuels, the cutting of forests, and manufacturing processes. Other greenhouse gases are also increasing in concentration in the atmoshpere. One of these is methane (cows and termites are major producers), nitrous oxide, and sulfur dioxide (automobile and industrial pollution).

Whether the increasing greenhouse gases are responsible or not, there is convincing evidence that global warming is certainly underway.

9



10


1

M. Dželalija, PhysicsCONTENTS Heat and Internal Energy

A major distinction must be made between internal energy and heat. Internal energy is all of the energy belonging to a system while it is stationary (neither translating nor rotating), including heat as well as nuclear energy, chemical energy, and strain energy. Thermal energy is the portion of internal energy that changes when the temperature of the system changes. Heat transfer is caused by a temperature difference between the system and its surrundings. We shawed that the thermal energy of a monoatomic ideal gas is associated with the motion of its atoms. In this special case, the thermal energy is simply kinetic energy on a microscopic scale. In general, thermal energy includes other forms of molecular energy, such as rotational energy and vibrational kinetic and potential energy.

The work done on (or by) a system is a measure of the energy transferred between the system and its surroundings. When a person does work on a system, energy is transferred from the person to the system. It makes no sense to talk about the work of a system – one shuld refer only to the work done on or by a system when some process has occurred in which energy has been transferred to or from the system. Likewise, it makes no sense to use the term heat unless energy has been transferred as a result of a temperature difference.

M. Dželalija, PhysicsCONTENTS Work

2

M. Dželalija, PhysicsCONTENTS Heat

The heat transferred into or out of a system is also found to depend on the process. This can be demonstrated by the situations depicted in figures. In each case, the gas has the same initial volume, temperature, and pressure, and is assumed to be ideal. In one figure, the gas expands slowly by absorbing heat from a reservoir at the same temperature. In other figure, the gas expands rapidly into an evacuated region after a membrane separating it from that region is broken. In both cases temperatures remain constant.

The initial and final states of the ideal gas in one figure are identical to the initial and final states in other figure, but processes are different. In the first case, heat is transfered slowly to the gas, and the gas does work on the piston. In the second case, no heat is transferred, and the work done is zero. Therefore, we conclude that heat transfer, like work, depends on the initial, final, and intermediate states of the system.

M. Dželalija, PhysicsCONTENTS The First law of Thermodinamics

3

M. Dželalija, PhysicsCONTENTS The Second Law of Thermodinamics

M. Dželalija, PhysicsCONTENTS Reversible and Irreversible Processes

A reversible process is one in which every state between the initial and final states is an equilibrium state, and that can be reversed in order to be followed exactly from the final state back to the initial state. A process that does not satisfy these requirements is irreversible.

All natural processes are known to be irreversible. But some are almost reversible. If a real process occurs very slowly so that the system is virtually always in equilibrium, the process can be considered reversible.

A general characteristic of a reversible process is that no dissipative effects that convert mechanical energy to thermal energy, such as turbulence or friction, can be present. In reality, such effects are impossible to eliminate completely, and hence it is not surprising that real processes in nature are irreversible.

4

M. Dželalija, PhysicsCONTENTS The Carnot Engine .

Sadi Carnot showed that a heat engine operating in an ideal, reversible cycle (called Carnot cycle) between two reservoirs is the most efficient engine possible.

No real engine operating between two heat reservoirs can be more efficient than a Carnot engine, operating between the same two reservoirs.

The cycle consists of two adiabatic and two isothermal processes, all reversible.

M. Dželalija, PhysicsCONTENTS The Carnot Engine ..

5

M. Dželalija, PhysicsCONTENTS Entropy

M. Dželalija, PhysicsCONTENTS Statistical View of Entropy

6



7



8


M. Dželalija, PhysicsCONTENTS Exercises ,.

What is wrong with the statement: “Given any two bodies, the one with the higher temperature contains more heat”?Heat is energy in the process of being trensferred, not a form of energy that is held or contained. Correct statement would be: (1) “Given any two objects in thermal contact, the one with the higher temperature will transfer heat to the other.” or (2) “Given any two objects of equal mass, the one with the higher products of absolute temperature and specific heat contains more internal energy.”A thermodinamic process occurs in which the entropy of a system changes by –10 J/K. According to the second law of thermodynamics, what can you conclude about the entropy change of the environment?The environment must have an entropy change of +10 J/K or more.

1

M. Dželalija, Physics (Part 12)CONTENTS Electric Charges .

A number of simple experiments demonstrate the existance of electrostatic forces. For example, after running a plastic comb through your hair, you will find that the comb attracts bits of paper. When materials behave in this way, theyare said to have become electrically charged. You can give your body an electric charge by sliding across a cat seat. You can then feel, and remove, the charge on your body by lightly touching another person. Under the right conditions, a visible spark can be seen when you touch, and a slight tingle is felt by both parties.

M. Dželalija, Physics (Part 12)CONTENTS Electric Charges ..

Experiments also demonstrate that there are two kinds of electric charge, which Benjamin Franklin named positive and negative. A rubber rod that has been rubbed with fur is suspended by a piece of string. When a glass rod that has been rubbed with silk is brought near the rubber rod, the rubber rod is attracted toward the glass rod. If two charged rubber rods (or two charged glass rods) are brought near each other, the force between them is repulsive. This observation demonstrates that the rubber and glass have different kinds of charge (on the glass rod is called positive, and on the rubber rod negative).

2

M. Dželalija, Physics (Part 12)CONTENTS Electric Charges ..

We now know that origin of charge is atom. Nature’s basis carrier of positive electricity is the proton located in the nucleus of an atom, and protons never moved from one material to another. Thus, when an object becomescharged, it does so because it has either gained or lost nature’s basic carrier of negative electricity, the electron.

An important characteristic of charge is that electric charge is always conserved. One object gains some amount of negative charge while the other loses an equal amount of negative charge and hence is left with a positive charge. For example, when a glass rod is rubbed with silk, the silk obtains a negative charge that is equal in magnitude to the positive charge on the glass rod as negatively charged electrons are transferred from the glass to the silk in the rubbing process. Likewise, when rubber is rubbed with fur, electrons are transferred from the fur to the rubber.

In 1909 Robert Millikan discovered that the charge is quantizied. This means that charge occurs as discrete bundles in nature. Thus, an object may have a charge of ±e, ±2e, and so on. An electron has a charge of –e. The value of e is now known to be C 106.1 19−⋅

M. Dželalija, Physics (Part 12)CONTENTS Insulators and Conductors

It is convinient to classify substances in terms of their ability to conduct electric charge.

Conductors are materials in which electric charges move freely, and insulators are materials in which electric charges do not move freely.

Glass and rubber are insulators. When such materials are charged by rubbing, only the rubbed area becomes charged, and there is no tendency for the charge to move into other regions of the material. In contrast, materials such as copper, aluminium, silver, or gold are good conductors. When such materials are charged in some small region, the charge readily distributes itself over the entire surface of the material.

Semiconductors are third class of materials, and their electrical properties are somewhere between those of insulators and those of conductors. Silicon and germanium are well-known semiconductors that are widely used in the fabrication of a variety of electronic devices.

3

M. Dželalija, Physics (Part 12)CONTENTS Coulomb’s Law

M. Dželalija, Physics (Part 12)CONTENTS The Electric Field

4

M. Dželalija, Physics (Part 12)CONTENTS Electric Field Lines

A convinient aid for visualizing electric field patterns is to draw lines pointing in the direction of the electric field vector at any point. These lines, called electric field lines, are related to the electric field in any region of space in the following manner:

The electric field vector is tangent to the electric field lines at each point.The number of lines per unt area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region.

Thus the magnitude of electric field is large when the field lines are close together and small when they are far apart.

M. Dželalija, Physics (Part 12)CONTENTS Conductors in Electrostatic Equilibrium

A good electric conductor, such as copper, contains charges (electrons) that are not bound to any atom and are free to move about within the material. When no net motion of charge occurs within a conductor, the conductor is said to be in electrostatic equilibrium.

It is possible to see that an isolated conductor (one that is insulated from ground) has the following properties:

the electric field is zero everywhere inside the conductor.Any excess charge on an isolated conductor resides entirely on its surface.The electric field just outside a charged conductor is prependicular to the conductor’s surface.On an irregularly shaped conductor, the charge tends to accumulate at locations where the radius of curvature of the surface is smallest. That is, at a sharp point.

Why is it safe to stay inside an automobile during a lightning storm?Although many people believe that this is safe because of the insulating

characteristics of the rubber tires, this is not true. Lighting is able to penetrate a centimeter of rubber. The safety of remaining in the car is due to the fact that charges on the metal shell of the car will reside on the outer surface of the car. Thus an occupant in the automibile touching the inner surfaces is not in danger.

5

M. Dželalija, Physics (Part 12)CONTENTS Electric Flux and Gauss’s Law

M. Dželalija, Physics (Part 12)CONTENTS Electrical Potential Energy

6

M. Dželalija, Physics (Part 12)CONTENTS Electric Potential

M. Dželalija, Physics (Part 12)CONTENTS Electric Potential Due to Point Charge

7

M. Dželalija, Physics (Part 12)CONTENTS Capacitance

A capacitor is a device used in a variety of electric circuits. For example, to tune the frequency of radio receivers, eliminate sparking in automobile ignition systems, or store short-term energy in electronic flash units.

It consists of two parallel metal plates separated by a distanceof d. When used in an electric circuit, the plates are connected to the positive and negative terminals of some voltage source. When this connection is made, electrons are pulled of one of the plates, leaving it with a charge of +Q, and other plates with –Q.

The capacitance,C, of a capacitor is defined as the ratio of the magnitude of thecharge on either conductor to the magnitude of the potential difference between the conductors

Large capacitence is needed to store a large amount of charge for a given applied voltage. Capacitence has SI units coulombs per volt, called farads 1F=1C/V. The farad is a very large unit of capacitance. In practice, most typical capacitors have capacitance ranging from microfarads to picofarads.

For example, the capacitance of a parallel-plate capacitor whose plates are separated by air is

where A is the area of one of the plates and d is the distance of the plates.

VQCΔ

=

space) free ofy permitivit is /NmC 1085.8( , 221200

−⋅== εεdAC

M. Dželalija, Physics (Part 12)CONTENTS Combinations of Capacitors

8

M. Dželalija, Physics (Part 12)CONTENTS Energy Stored in a Charged Capacitor

M. Dželalija, Physics (Part 12)CONTENTS Capacitors with Dielectrics

A dielectric is an insulating material, such as glass, rubber or waxed paper. When a dielectric is inserted between the plates of a capacitor, the capacitance increases. If the dielectric completely fills the space between the plates, the capacitance is multiplied by the factor κ, called the dielectric constant

)dielectric a of absence in the ecapacitanc theis ( 00 CCC κ=

9



10


If a suspended object A is attracted to object B, which is charged, can we conclude that object A is charged?No. Object A might have a charge opposite in sign to that of B, but it also might be a neutral conductor. In the later case, object B causes object A to be polarized, pulling charge of one sign to the near face of A and pushing an equal amount of charge of the opposite sign to the far face. Then the force of attraction exerted on B by the induced charge on the near side of A is slightly larger than the force of repulsion exerted on B by the induced charge on the far side of A. Therefore, the net force on A is toward B.If a metal object receives a positive charge, does its mass increase, decrease, or stay the same? What happens to its mass if the object receives a negative charge?An object’s mass decreases very slightly (immeasurably) when it is given a positive charge, because it loses electrons. When the object is given a negative charge, its mass increases slightly because it gains electrons.In fair weatherm there is an electric field at the surface of the Earth, pointing down into the ground. What is the electric charge on the ground in this situations?Electric field lines start on positive charges and end on negative charges. Thus, if the fair weather field is directed into the ground, the ground must have a negative charge.


11

M. Dželalija, Physics (Part 12)CONTENTS Exercises .....

1

M. Dželalija, Physics (Part 13)CONTENTS Electric Current

M. Dželalija, Physics (Part 13)CONTENTS Resistance and Ohm’s Law

2

M. Dželalija, Physics (Part 13)CONTENTS Resistivity

The resistivity, and hence the resistance, of a conductor depends on a number of factors. One of the most important is the temperature of the metal. For most metals, resistivity increases with increasing temperature.

Good electric conductors have very low resistivity, and good insulators have very high resistivity. Table lists the resistivities of a variety of materials at 20°C.

M. Dželalija, Physics (Part 13)CONTENTS Electric Energy and Power

3

M. Dželalija, Physics (Part 13)CONTENTS Combinations of Resistors


Electrical devices are often rated with a voltage and a current (for example, 120 V, 5 A). Batteries, however, are only rated with a voltage (for example, 1.5 V). Why?An electrical appliance has a given resistance. Thus, when it isattached to a power source with a known potential difference, a definite current will be drawn. The device can be labeled with both the voltage and the current. Batteries, however, can be applied to a number of devices. Each device will have a different resistance, so the current from the battery will vary with the device. As a result, only the voltage of the battery can be specified.Why is it possible for a bird to sit on a high-voltage wire without being electrocuted?The bird is resting on a wire of a fixed potential. In order to be electrocuted, a potential difference is required. There is no potential(very low) difference between the bird’s feet.

4



5

M. Dželalija, Physics (Part 13)CONTENTS Magnets

Most people have had experience with some form of magnet. Iron objects are most strongly attracted to the ends of magnet, called its poles. One end is called the north pole and the other the south pole. The names come from the behaviour of a magnet in the presence of the Earth’s magnetic field (north pole points to the north of the Earth).

Magnetic poles also exert attractive or repulsive forces on each other similar to the electrical forces between charged objects. Like poles repel each other and unlike poles attract each other.

Electric charges can be isolated, but magnetic poles cannot. Magnetic poles always occur in pairs.

Magnetism can be induced in some materials. For example, if a piece of unmagnetized iron is placed near a strong permanent magnet, the piece of iron eventually becomes magnetized. Iron is easily magnetized but also tend to lose their magnetism easily. In contrast, cobalt and nickel are difficult to magnetize but tend to retain their magnetism.

Recall that an electric field surrounds any electric charge. The region of space surrounding a moving charge also includes a magnetic field.

M. Dželalija, Physics (Part 13)CONTENTS Magnetic Field of the Earth

The geografic north pole corresponds to a magnetic south pole, and the geografic south pole corresponds to a magnetic north pole.

If a compass needle is suspended in bearings that allow it to rotate in the vertical plane as well as in the horizontal plane, the needle is horizontal with respect to the Earth’s surface only near the Equator. As the device is moved northward the needle rotates so that it points more and more toward the surface of the Earth.Finally, at a point justnorth of Hudson Bay inCanada, the north pole of the needle points directly downward. It is about 2000 km from the Earth’s geografic north pole and varies with time. Thus it is onlyapproximately correct to say that a compass needle point north.

6

M. Dželalija, Physics (Part 13)CONTENTS Magnetic Fields

Stationary charged particle does not interact with a static magnetic field. However, when moving through a magnetic field a charged particleexperiences a magnetic force. This force has its maximum value when the charge moves perpendicularly to the magnetic field lines. It becomes zero when the particle moves along the field lines.

The SI unit if magnetic field is the tesla (T). For example, the Earth’s magnetic field near its surface is abut 0.00005 T.

From a simple experiment it is possible to demonstrates that a current-carrying conductor produces a magnetic field (first found by Oersted, 1820).

M. Dželalija, Physics (Part 13)CONTENTS Solenoid

If a long straight wire is bent into a coil of several closely spaced loops, the resulting device is a solenoid. This device is important in many applications because it acts as a magnet only when it carries a current. The magnitude of the magnetic field B inside a solenoid increases with the current I and is proportional to the number of coils per unit length N/l

space) free ofity (permeabilTm/A 104 , 700

−⋅== πμμ IlNB

7

M. Dželalija, Physics (Part 13)CONTENTS Exercises

Why does the picture on a television screen become distorted when a magnet is brought near the screen? (You should not do this at home on a color television set, because it may permanently affect the television picture quality.)The magnetic field of the magnet produces a magnetic force on the electrons moving toward the screen that produce the image. This magnetic force deflects the electrons to regions on the screen other than the ones to which they are supposed to go. The result is a distorted image.Can you use a compass to detect the currents in wires in the walls near light switches in your home? A compass would not detect currents in wires near light switches for two reasons. Because the cable to the light switch contains two wires, with one carrying current to the switch and the other away from the switch, the net magnetic field would be very small and fall off rapidly. The second reason is that the current is alternating at 50 Hz. As a result, the magnetic field is oscillating at 50 Hz, also. This frequency would be too fast for the compass to follow, so the effect on the compass reading would average to zero.

1

M. Dželalija, Physics (Part 14)CONTENTS Maxwell’s Predictions

In 1865 James Clerk Maxwell provided a mathematical theory that showed a close relationship between electric and magnetic phenomena. His theory predicted that electric and magnetic fields can move through space as waves. The theory he developed is based onthe following:

Electric field lines originate on positive charges and terminate on negative charges.Magnetic field lines always form closed loops.A varying magnetic field induces an electric field.Magnetic fields are generated by moving charges (or currents) or by a varying electric fields.

The waves sent out by the oscillating charges are fluctuating electric and magnetic fields, and so they are called electromagnetic waves, traveling through empty space with a speed of about 300 000 000 m/s.

In 1887, Heinrich Hertz was the first to generate and detect electromagnetic waves in a laboratory setting.

M. Dželalija, Physics (Part 14)CONTENTS Production of Electromagnetic Waves .

Electromagnetic waves are radiated by any circuit carrying an alternating current. The fundamental mechanism responsible for this radiation is the acceleration of a charged particle. Whenever a charged particle undergoes an acceleration, it must radiate energy.

An alternating voltage applied to the wires of an antenna forces an electric charge in the antenna to oscillate. This is a common technique for accelerating charged particles and is the source of the radio waves emitted by the broadcast antenna of a radio station. As the charges continue to oscillate between the rods, the electric field moves away from the antenna at the speed of light.

2

M. Dželalija, Physics (Part 14)CONTENTS Production of Electromagnetic Waves .

Because the oscillating charges create a current in the rods, a magnetic field is also generated. The magnetic field lines circle the antenna and are perpendicular to the electric field at all points. Both fields are perpendicular to the direction of motion of the wave. Hence, we see that an electromagnetic wave is a transverse wave.

At great distance from the antenna, the strengths of he electric and magnetic fields become very weak.

M. Dželalija, Physics (Part 14)CONTENTS Properties of Electromagnetic Waves

3

M. Dželalija, Physics (Part 14)CONTENTS The Spectrum of Electromagnetic Waves .

All electromagnetic waves travel through vacuum with a speed of c. Hence, their frequency, f, and wavelength, λ, are related by the expression

fc λ=

M. Dželalija, Physics (Part 14)CONTENTS The Spectrum of Electromagnetic Waves ..

The types of electromagnetic waves are (there are no sharp division between one kind of wave and the next):

Radio waves, are the result of charges accelerating through conduction wires. They are used in radio and television communication systems.Microwaves, have wavelengths ranging between about 1 mm and 30 cm, and are generated by electronic devices. They are well suited for the radar systems used in aircraft navigation. Microwave ovens are an interesting domestic application.Infrared waves (sometimes called heat waves), produced by hot bodies and molecules, have wavelengths ranging from about 1 mm to the longest wavelength of visible light, 700 nm. They are readily absorbed by most materials. The infrared energy absorbed by a substance appears as heat. This is because the energy agitates the atoms of the object, increasing their vibrational or translational motion, and the result is a temperature rise. Physical therapy and infrared photography are some practical applications.

4

M. Dželalija, Physics (Part 14)CONTENTS The Spectrum of Electromagnetic Waves ...

Visible light, the most familiar form of electromagnetic waves, may be defined as the part of the spectrum that is detected by a human eye. Light is produced by the rearrangement of electrons in atoms and molecules. The wavelength of visible light are classified as colors ranging from violed, 400 nm, to red, 700 nm. The eye’s sensitivity is a function of wavelength and is greatest at a wavelength of about 560 nm (yellow-green).

M. Dželalija, Physics (Part 14)CONTENTS The Spectrum of Electromagnetic Waves ....

Ultraviolet light (UV) covers wavelengths ranging from about 400 nm to 0.6 nm. The Sun is an important source of ultraviolet light (which is the main cause of suntans). Most of the ultraviolet light from the Sun is absorbed by atoms in the upper atmosphere, or stratosphere. This is fortunate, because UV light in large quantities has harmful effects on humans. One important constituent of the stratosphere is ozone from reactions of oxygen with ultraviolet radiation. This ozone shield converts lethal high-energy ultraviolet radiation to heat, which warms the stratosphere.X-rays are electromagnetic waves with wavelengths from about 10 nm to 0.1 pm. The most common source of x-rays is the acceleration of high-energy electrons bombarding a metal target. X-rays are used as a diagnostic tool in medicine and as a treatment for certain forms of cancer. Because x-rays damage or destroy living tissues and organisms, care must be taken to avoid unnecessary exposure and overexposure.Gamma rays are emitted by radioactive nuclei. They are highly penetrating and cause serious damage when absorbed by living tissues. Those working near such radiation must be protected by garments containing heavily absorbing materials, such as layers of lead.

5


1

M. Dželalija, Physics (Part 15)CONTENTS The Nature of Light

Until the beginning of the 19th century, light was considered to be a stream of particles, emitted by a light source, that stimulated the sence of sight on entering the eye. That was proposed by Newton.

During Newton’s lifetime Christian Huygens proposed another theory – wave theory of light. The wave theory did not receive immediate acceptance because there were not clear experimental evidence and also due to Newton’s great reputation as a scientist. The first clear demonstration of the wave nature of light was provided in 1801 by Thomas Young, who showed that light exhibits interference behavior. That is, for example, at certain points in the vicinity of two sources, light waves can combine and cancel each other by destructive interference.

The most important development concerning the theory of light was the work of Maxwell, who in 1865 predicted that light was a form of electromagnetic wave. Althought his theory explained most known properties of light, some subsequent experiments could not be explained by the assumption that light was a wave. The most striking of these was the photoelectric effect (clean metal surfaces emit charges when exposed to ultraviolet light).

In 1905 Einstein formulated theory of light quanta and explained the photoelectric effect. He conclused that light is composed of corpuscles (photons) with energy proportional to the frequency of the electromagnetic wave, E=hf, where h is Planck’s constant.

Thus, light must have a dual nature. That is, in some cases light acts as a waveand in others as a particle, but never acts as both in the same experiments.

M. Dželalija, Physics (Part 15)CONTENTS The Speed of Light

Light travels so fast that early attempts to measure its speed were unsuccessful. The first known successful estimate of the speed of light was made in 1675 by Ole Roemer. His technique involved astronomical observations of one of the moons of Jupiter, Io. He estimated the speed of light to be about 210 000 km/s.

Later, in 1849, Fizeau arrived at a value of 310 000 m/s.A recent value of the speed of light in a vacuum, obtained using a laser

technique, is 299 792 458 m/s.

2

M. Dželalija, Physics (Part 15)CONTENTS Geometric Optics

Firstly, our discussion of light will be concerned with what happens when light passes through some optic materials or reflects from them (lenses, mirrors, etc). Explanations of such phenomena can be done by geometrical analysis of light rays. That part of optics is often called geometric optics.

First property of light, inside geometric optics, can be understood based on common experience: light travels in a straight line path until it encounters a boundary between two different materials. When light strikes a boundary it either is reflected from the boundary, passes into the material on the other side of the boundary, or partially does both.

We use the ray approximation to represent beams of light.

M. Dželalija, Physics (Part 15)CONTENTS Reflection of Light

When a light ray traveling in a transparent medium encounters a boundary leading into a second medium, part (or total) of the incident ray is reflected back into first medium. Reflection of light from a smooth surface is called specular reflection. If the reflecting surface is rough, the surface reflects the rays in a variety of directions. Reflections from any rough surface is known as diffuse reflection. We will concern ourselves only with specular reflection, and we use term reflectionto mean specular reflection.

Experiments show that the angle of reflection equals the angle of incidence, that is,

1'

1 θθ =

3

M. Dželalija, Physics (Part 15)CONTENTS Refraction of Light

When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the ray enters the second medium, and is said to be refracted.

Experiments show that the angle of refraction depends on the properties of the two media and on the angle of incidence as

where are indices of refraction of two mediums, defined as

law) sSnell' (called sinsin 2211 θθ nn =

21 and nn

vcn ==

medium ain light of speedin vacuumlight of speed

M. Dželalija, Physics (Part 15)CONTENTS Indices of Refraction

From the definition, we see that the index of refraction is a dimensioless number that is greater than 1, because speed of light in any medium is less than speed of light in vacuum. (For a vacuum index equals 1.)

It is possible to show that, as light travels from one medium to another, its wavelength changes but its frequency remains constant.

4

M. Dželalija, Physics (Part 15)CONTENTS Dispersion of Light

An important property of the index of refraction is that its value in anything but vacuum depends on the wavelength of light. This phenomena is called dispersion. Using Snell’s law we can see that light of different wavelengths is bent at different angles when incident on a refracting material. Blue light (~470 nm) bends more than red light (~650 nm) when passing into a refracting material.

Suppose a beam of white light (a combination of all visible wavelengths) is incident on a prism. Because of dispersion, the rays that emerge from the second face of the prism fan out in a series of colors known as a visible spectrum.

M. Dželalija, Physics (Part 15)CONTENTS The Rainbow

The dispersion of light into a spectrum is demonstrated most vividly in nature through the formation of a rainbow, often seen by an observer positioned between the Sun and a rain shower. A ray of light passing overhead strikes a drop of water in the atmosphere and is refracted and reflected as shown in figure. The small angular difference between the returning violet and red rays causes us to see the bow.

5

M. Dželalija, Physics (Part 15)CONTENTS Total Internal Reflection

An interesting effect called total internal reflection can occur when light attempts to move from a medium with a high index of refraction to one with a lower index of refraction. At some particular angle of incidence, called the critical angle, the refracted light ray moves parallelto the boundary. For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary.

Interecting applications are submarine periscopes and fiber optics (in medicine and telecommunications)


Tape a coin to the bottom of a large opaque bowl as in figure. Look at the coin from the side and move backwards until you can no longer see the coin. Remain still at that position, and have a friend pour water into the bowl until it is full as in figure. Nore that you are now able to see the coin because the light is refracted at the water-air interface.

6


1

M. Dželalija, Physics (Part 16)CONTENTS Flat Mirrors

A distance, p, of a point light source (called object)in front of a flat mirror is called the object distance. Light rays leave the source and are reflected from the mirror. After reflection, the reysdiverge (spread apart), but they appear to theviewer to come from a point behind the mirror,called the image of the object. Images areformed at the point at which rays of light actuyllyintersect or at which they appear to originate. A distance, q, of the image is called image distance.

Images are classified as real or virtual. A real image is one in which light actually intersects, or passes through, the image point; a virtual image is one in which the light does not pass through the image point but appears to come (diverge) from that point. The image formed by the flat miror in the figure is a virtual image. Real images can be displayed on a screan, but virtual images cannot.

The image formed by an object placed in front of a flat mirror is as far behind the mirror as the object is in front of the mirror, p=q.

M. Dželalija, Physics (Part 16)CONTENTS Spherical Mirrors

A spherical mirror has the shape of a segment of a sphere. A spherical mirror with light reflecting from its inner concave surface is called a concave mirror. The mirror has radius of curvature R, and its center of curvature is at point C.

A spherical mirror that light is reflected from the outer convex surface is called convex mirror.

Using simple algebra it is possible to get the expression called the mirror equation

where f is the focal length defined as f = R/2.For the magnification of the mirror we can find

fqp111

=+

pq

hhM −===

'heightobject height image

2

M. Dželalija, Physics (Part 16)CONTENTS Refracting Surfaces

Using Snell’s law of refraction and simple geometrical techniques it is possible to show that, if the refracting surface is flat, the object distance and image distance are related by the equation

Forthermore, the magnification of a refracting surface is

)refraction of indices are ,( 2121 nn

qn

pn

−=

pnqn

hhM

2

1'heightobject height image

−===

M. Dželalija, Physics (Part 16)CONTENTS Mirage and Halo

The mirage is phenomenon of nature produced by refraction in the atmosphere. A mirage can be observed when the ground is so hot that the air directly above it is warmer than the air at higher elevations. The desert is a region in which such circumstances prevail, but mirages are also seen on heated roadways during the summer. The layers of air at different heights above the Earth have different densities and different refractive indicies.

A halo around Moon is another phenomenon of nature. These halos are most commonly seen on winter nights because an abundance of ice crystals in the sky is necessary for their production. When a light ray passes through, it is deflected by an angle of about 22°.

3

M. Dželalija, Physics (Part 16)CONTENTS Thin Lenses

A typical thin lens consists of a piece of glass or plastic, ground so that each ofits two refracting surfaces is a segment of either a sphere or a plane. Lenses are commonly used to form images by refraction in optical instruments, such as cameras, microscopes, and telescopes. The equation that relates object and images distances for a lens

is virtually identical to the mirror equation.Lenses can be placed in two groups. The lenses that are

thicker at the center than at the tim are called converging lenses, and those that are thinner at the center than at the rim are diverging lenses.

fqp111

=+

M. Dželalija, Physics (Part 16)CONTENTS Focal Length

The focal length, f, is defined as the image distance that corresponds to an infinite object distance. Note that a converging lens has a positive focal length, and a diverging has a negativefocal length. Hence the names positive and negative are often given to those lenses.

The focal length for a lens in air is related to the curvatures of its front and back surfaces and to the index of refraction of the lens material by

⎟⎟⎠

⎞⎜⎜⎝

⎛−−=

21

11)1(1RR

nf

4

M. Dželalija, Physics (Part 16)CONTENTS Lens Aberrations

One of the basic problems of lenses is the imperfect quality of the images. The departures of real (imperfect) images from the ideal predicted by the simple theory are called aberrations. Two common types of abrreations are spherical and chromatic aberrations.

Spherical aberration results from the fact that the focal points of light rays far from the principal axis of a spherical lens (or mirror) are different from the focal points of rays passing near the axis. In the case of mirrors one can minimize spherical aberration by employing a parabolic rather than spherical surface (but they are very expensive).

The fact that different wavelenghts of light refracted by a lens focus at different points rise to chromatic aberration. When light passes through a lens, for example, voilet light rays are refracted more than red light rays. Chromatic aberration can be greatly reduced by the use of a combination of converging and diverging lenses made from two different types of glases.


5



6


M. Dželalija, Physics (Part 16)CONTENTS Exercises .....

7

M. Dželalija, Physics (Part 16)CONTENTS Exercises ,.

1

M. Dželalija, Physics (Part 17)CONTENTS Interference

Our discussion of light has been concerned with what happens when light passes through a lens or reflects from a mirror. Explanations of such phenomena rely on a geometric analysis of light rays. That part of optics is called geometric optics. Interference, diffraction, and polarization are phenomena that cannot be adequatly explained with ray optics, but the wave theory leads us to satisfying description. That part of optics we call wave optics.

In our discussion of interference of mechanical waves (Part 7), we found that two waves could add together either constructively or descructively. In conscructive interference, the amplitude of the resultant wave is greater than that of either of the individual waves, whereas in descructive interference, the resultant amplitude is less than that of either individualwave. Electromagnetic waves also undergo interference. Furthermore, all interference associated with electromagnetic waves arises from the combining of the electric and magnetic fields that constitute the individual waves.

Interference effects in light waves are not easy to observe because of the short wavelengths involved (about 400-750 nm). For sustained interference between two sources of light to be observed, the sources must contain a constant phase with respect to each other (must be coherent), and must have identical wavelengths.

M. Dželalija, Physics (Part 17)CONTENTS Diffraction

If the light truly traveled in straight-line paths after passing through the slits, the waves would not overlap and no interference pattern would be seen. But, the light deviates from a straight-line path and enters the region that would otherwise be shadowed. This divergence of light from its initial line of travel is called diffraction.

In general, diffraction occurs when waves pass through small opening, around obstacles, or by sharp edges. This phenomena cannot be explained within the framework of geometric optics, which says that light rays traveling in straight lines.

2

M. Dželalija, Physics (Part 17)CONTENTS Polarization

We described the transverse nature ofelectromagnetic waves. The electricand magnetic field vectors asociatedwith an electromagnetic wave are atright angles to each other and alsoto the direction of wave propagation.

An ordinary beam of light consists of a large number of waves emitted by the atoms or molecules of the light source. Each atom produces a wave with its own orientation of electric field vector, corresponding to the direction of atomic vibration. However, because all directions of vibration are possible, the resultant electromagnetic wave is a superposition of waves produced by the individual atomic sources. The result is an unpolarized light wave.

A wave is said to be lineraly polarized if electric field vector is in the same direction at all times at a particular point.

M. Dželalija, Physics (Part 17)CONTENTS Polarization by Selective Absorbers

The most common technique for polarizing light is to use a material that transmits waves whose electric field vectors are in a plane parallel to a certain direction and absorbs those waves whose electric field vectors are in directions perpendicular to that direction.

In 1932, Land discovered a material, called polaroid, that polarizes light through selective absorption by oriented molecules. This material is fabricated in thin sheets of long-chain hydrocarbons. The molecules absorb light whose electric field vector is perpendicular to their lengths.

3

M. Dželalija, Physics (Part 17)CONTENTS Polarization by Reflection .

When an unpolarized light beam is reflectedfrom a surface, the reflected light is completely polarized, partially polarized,or unpolarized, depending on the angle of incidence. If the angle of incidence iseither 0° or 90°, the reflected beam is unpolarized. However, for angles ofincidence between 0° or 90°, the reflected light is polarized to some extent. For one particular angle of incidence, the reflected beam is completely polarized. This angle is called the polarizing angle (or Brewster’s angle), and it is valid

where n is relative index of refraction. This occurs when the angle between the reflected and refracted beams is 90°.

np =θtan

M. Dželalija, Physics (Part 17)CONTENTS Polarization by Reflection .

Polarization by reflection is a common phenomena. Sunlight reflected from water, glass, or snow is partially polarized. If the surface is horizontal, the electric field vector of the reflected light has a strong horizontal component. Sunglasses made of polarizing material reduce the glare of reflected light.

4

M. Dželalija, Physics (Part 17)CONTENTS Polarization by Scattering

When light is incident on a system of particles, such as a gas, the electrons in the medium can absorb and reradiate part of light. The absorption and reradiation of light by the medium, called scattering, is what causes sunlight reaching an observer on the Earth from straight overhead to be polarized. You can observe this effect by looking directly up through a pair of sunglasses made of polarizing glass. Less light passes through at certain orientations of the lenses than at others.

Bees and homing pigeons use the polarization of sunlight as a navigational aid.

M. Dželalija, Physics (Part 17)CONTENTS The Camera

The single-lens photographic camera is a simple optical instrument whose essential features are shown in figure. It consists of a light-tight box, a converging lens that produces a real image, and a film behind the lens to receive the image. For proper focusing, which leads to sharp images, the lens-to-film distance will depend on the object distance as well as on the focal length of the lens. The shutter, located behind the lens, is a mechanical device that is opened for selected time intervals. With this arrangement, moving objects can be photographed with the use of short exposure times, and dark scenes with the use of long exposure times.Typical shutter times are 1/30, 1/60, 1/125, and 1/250 s.

5

M. Dželalija, Physics (Part 17)CONTENTS The Eye .

Like the camera, the eye gathers light and produces a sharp image. The front of the eye is covered by a transparent membrane called the cornea. Inward from the cornea are a clear liquid region (the aqueous humur), a variable aperture (the iris surrounding the pupil), and the crystalline lens. Most of the refraction occurs in the cornea, because the liquid medium surrounding the lens has an average index of refraction close to that of the lens. The iris, the colored portion of the eye, is a muscular diaphragm that regulates the amount of light entering the eye by dilating the pupil (increasing its diameter) in light of low intensity and contracting the pupil in high-intensity light.

M. Dželalija, Physics (Part 17)CONTENTS The Eye ..

Light entering the eye is focused by the cornea-lens system onto the back surface of the eye, called the retina. The surface of the retina consists of millions of sensitive receptors called rods and cones. When stimulated by light, these structures send impulses via the optic nerve to the brain, where a distinct image of an object is perceived.

The eye focuses on a given object by varying the shape of the pliable crystalline lens through an amazing process called accommodation. An important component in accommodation is the ciliary muscle, which is attached to the lens. It is evident that there is a limit to accomodation, because objects that are very close to the eye produce blurred images. The near point is the smallest distance for which the lens will produce a sharp image on the retina. This distance usually increases with age.

6

M. Dželalija, Physics (Part 17)CONTENTS Defects of the Eye

An eye can have several abnormalities that keep it from functioning properly. When the relaxed eye produces an image of a nearby object behind the retina, the abnormality is known as hyperopia, and the person is said to be farsighted. With this defect, distant object are seen clearly but near object are blurred. Either the hyperopic eye is too short or the ciliary muscle cannot change the shape of the lens enough to focus the image properly. The condition can be corrected with a converging lens.

Another condition, known as myopia, or nearsightedness, occurs when a distant object is focused in front of the retina. This can be corrected with a diverging lens.

A common eye defect is astigmatism, in which light from a point source produces a line image on the retina. This occurs when the cornea or the lens are not perfectly spherical. A cylindrical lens is used to correct this.

M. Dželalija, Physics (Part 17)CONTENTS The Power

The power, P, of a lens in diopters equals the inverse of the focal length inmeters. That is, P=1/f.

For example, a converging lens whose focal length is +20 cm has a power of 1/(+0.2 m)=+5 diopters, and a diverging lens whose focal length is –40 cm has a power of 1/(-0.4 m)=-2.5 diopters.

7



1

M. Dželalija, Physics (Part 18)CONTENTS Relativity

Most of our everyday experiences and observations deal with objects that move at speeds much lower than the speed of light. Newtonian mechanics and the early ideas on space and time were formulated to describe the motion of such objects. Although Newtonian mechanics works very well at low speeds, it fails when applied to particles whose speeds approach that of light.

In 1905, Einstein published his special theory of relativity which covers such phenomena. This theory is based on two postulates:

The laws of physics are the same in all inertial reference systems.The speed of light in a vacuum is always measured to be 300 000 km/s, and the measured value is independent of the motion of the observer or of the motion of the source of light.

M. Dželalija, Physics (Part 18)CONTENTS Relativistic Momentum and Energy

Within the framework of Einstein’s postulates of relativity, it is found that momentum is not conserved if the classical definition of momentum, p=mv, is used. However, according to the principle of relativity, momentum must be conserved in all reference systems. The correct relativistic equation for momentum that satisfies these conditions is

where v is the velocity of the particle.

It is also found that the minimum energy of some object is

E=mc²

called the rest energy, where m is mass of the object and c is speed of the light. This famous mass-energy equivalence equation shows that mass is one possible manifestation of energy. It shows that a small mass corresponds to an enormous amount of energy.

/1 22 cv

mvp−

=

1

M. Dželalija, Physics (Part 19)CONTENTS Blackbody Radiation

A modern version of mechanics called quantum physics was highly successful in explaining the behaviour of atoms, molecules, and nuclei. The earliest and most basic ideas of quantum theory were introduced by Planck. Anextensive study of quantum theory is beyond the scope of this course, as well as relativistic theory. We will only underly ideas of quantum theory.

An object at any temperature is known to emit radiation (Stefan’s law, Part 10). The spectrum of the radiation depends on the temperature and properties of the object. At low temperatures, the wavelengths of the thermal radiation are mainly in the infrared region and hence not observable by the eye. As the temperature of an object increases, the object eventually begins to glow red. At sufficiently high temperatures, it appears to be white. With increasing temperature, the peak of the distribution shifts to shorter wavelengths. This shift was found to obey the following relationship, called Wien’s law

mK 10898.2 3max

−⋅=Tλ

M. Dželalija, Physics (Part 19)CONTENTS Planck’s Hypothesis

Early attempts to use classical ideas to explain the blackbody radiation failed. In 1900 Planck developed a formula for blackbody radiation that was in complete agreement with experiments. He made assumption that submicroscopic electric oscillators can emit discrete units of light energy that are called photons with energy of

f is the frequency of an electric oscillator (and light emitted).The key point in Planck’s theory is the radical assumption of quantizied

energy states.

constant) sPlanck' is Js 10626.6( 34−⋅== hhfE

2

M. Dželalija, Physics (Part 19)CONTENTS The Photoelectric Effect

Experiments showed that, when light is incident on certain metallic surfaces, electrons are emitted from the surface. This phenomenon is known as the photoelectric effect. According to photoelectric effect equation (introduced by Einstein) the kinetic energy for those liberated electrons is

where W is called the work function of the metal. The work function represents the minimum energy with which an electron is bound in the metal.

Many practical devices in our everyday lives depend on the photoelectric effect. For example, a use familiar to everyday is that of turning street lights on at night and off in the morning. A photoelectric control unit in the base of the light activates a switch to turn off the streetlight when ambient light of the correct frequency falls on it.

WhfEk −=

M. Dželalija, Physics (Part 19)CONTENTS The Wave Properties of Particles

In 1923 Louis de Broglie postulated that because photons have wave and particle characteristics, perhaps all forms of matter have wave as well as particle properties. He suggested that material particles, of momentum p, should also have wave properties and a corresponding wavelength λ

This proposal was first regarded as pure speculation. But in 1927 Davisson and Germer succeeded in measuring the wavelength of electron.

ph

=λ

3

M. Dželalija, Physics (Part 19)CONTENTS The Electron Microscope

A practical device that relies on the wave characteristics of electrons is the electron microscope, which is in many respects similar to an ordinary compound microscope. One important difference is that the electron microscope has a much greater resolving power because electrons can be accelerated to high momentum, giving them a very short wavelength. Any sort of microscopes is capable of detecting details that are comparable in size to the wavelength of the radiation used to illuminate the object. The wavelengths of electrons typically are about 100 times shorter than those of the visible light used in optical microscopes. As a result, electron microscopes are able to distinguish details about 100 times smaller.

M. Dželalija, Physics (Part 19)CONTENTS The Uncertainty Principle .

If you were to mesuring the position and velocity of a particle at any instant, you would always be faced with reducing the experimental uncertainties in the measurements as much as possible.

According to classical mechanics, there is no fundamental barrier to an ultimate refinement of the apparatures or experimental procedures.

Quantum theory predicts, however, that it is impossible to make simultaneous measurements of a particle’s position and velocity with infinite accuracy. This statement, known as uncertainty principle, was first derived by Heisenberg in 1927.

4

M. Dželalija, Physics (Part 19)CONTENTS The Uncertainty Principle ..

Suppose that Δx and Δpx represent the uncertainty in the measured values of the particle’s position and momentum along the x axis at some instant. The uncertainty principle says that the product Δx Δpx, is never less than a number of the order of Planck’s constant h

That is, it is physically impossible to measure simultaneously the exact position and exact momentum of a particle.

π2hpx x ≥ΔΔ


5


1

M. Dželalija, Physics (Part 20)CONTENTS Early Models of the Atom

The model of the atom in the days of Newton was a tiny, hard, indestrucible sphere.

Thomson suggested a model of the atom as a volume of positive charge with electrons embedded throughout the volume.

Rutherford assumed that the positive charge in an atom was concentrated in a region that was small relative to the size of the atom, called the nucleus. Any electrons belonging to the atom were assumed to be in the volume outside the nucleus, moving in the same manner as theplanets orbit the Sun.

Using the simplest atom, hydrogen, Bohr proposed a model of the hydrogen atom based on a clever combination of classical and early quantum concepts. His basic assumption – that atoms exist in discrete quantum states of well-defined energy – was a bold break with classical ideas. In spite of its successes, Bohr’s specific model of the hydrogen atom was inconsistent with the uncertainty principle and was replaced by the probability density model derived fom Schrödinger’s work.

M. Dželalija, Physics (Part 20)CONTENTS Atomic Spectra

If a voltage applied between metal electrodes in the tube (filled with some gas), the tube emits light whose color is characteristic of the gas in the tube. When the emitted light is analyzed with a spectrometer, a series of lines is observed. Such a series of spectrallines is commonly referred to as anemission spectrum. The wavelengths contained in a given line spectrum are characteristic of the element emitting the light. Because no two elements emit the same line spectrum, this phenomenon represents a marvelous and reliable technique for identifying elements in a substance.

An element can also absorb light at specific wavelengths, known as absorption spectrum. The absorption spectrum consists of a series of dark lines superimposed on the otherwise continuous spectrum. Each line in the absorption spectrum of a given element coincides with a line in the emission spectrum of the element.

2

M. Dželalija, Physics (Part 20)CONTENTS Quantum Mechanics and the Hydrogen Atom

One of the first great achievements of quantum mechanics was the solution of the wave equation for the hydrogen atom. Three quantum numbers emerged from the solution of the wave equation

principal quantum number, n=1,2,3,...orbital quantum number, l=0,1,2,...,n-1orbital magnetic quantum number, ml =-l,...,l

It was later found that another quantum number, ms, the spin magnetic quantum number had to be introduced with two values, +½, -½.

M. Dželalija, Physics (Part 20)CONTENTS The Periodic Table

The state of an electron in an atom is specified by four quantum numbers, that we introduced (n, l, ml, ms). These quantum numbers can be used to describe all the electronic states of an atom regardless of the number of electrons in its structure. Obvoious question that arises is, how many electrons in an atom can have a particular set of quantum numbers. Pauli answered this in statetements known as the exclusion principle:no two electrons in an atom can ever be in the same quantum state; that is, no two electrons in the same atom can have the same set of quantum numbers.

Hydrogen has only one electron, which, in its ground state, can be described by either of two sets of quantum numbers: 1,0,0,+½ or 1,0,0,-½. The electronic configuration of this atom is designated as 1s¹. The notation 1s refers to a state for which n=1 and l=1, and the superscript indicates that one electron is present in this level. Neutral helium has two electrons. The quantum numbers are 1,0,0,+½ and 1,0,0,-½, with configuration 1s².

3

M. Dželalija, Physics (Part 20)CONTENTS Atomic Transitions .

An atom will emit radiation only at certain frequency that corresponds to the energy separation between the various allowed states. When light is incident on the atom, only those photons whose energy, hf, matches the energy separation ΔE between two levels can be absorbed by the atom (stimulated absorption process). As a result, some atoms are raised to various allowed higher energy levels, called excited states.

M. Dželalija, Physics (Part 20)CONTENTS Atomic Transitions ..

Once an atom is in an excited state, there is a constant probability that it will jump back to a lower energy level by emitting a photon. This process is known as spontaneous emission.

A third process that is important in lasers, stimulated emission, was predicted by Einstein in 1917. Suppose an atom is in the excited state and a photon with energy hf =ΔE is incident on it. The incoming photon increases the probability that the excited electron will return to the ground state and thereby emit a second photon having the same energy hf. These photons can stimulate other atoms to emit photons in a chain of similar processes. The many photons produced in this fashion are the source of the intense, coherent light in a laser.

1

M. Dželalija, Physics (Part 21)CONTENTS Some Properties of Nuclei

All nuclei are composed of two types of particles: protons and neutrons. In describing some of the properties of nuclei, such as their charge, mass, and radius, we make use of the following quantities:

the atomic number, Z, which equals the number of protons in the nucleusthe neutron number, N, which equals the number of neutrons in the nucleusthe mass number, A, which equals the number of nucleons in the nuclus. (Nucleon is a generic term used to refer to either a proton or a neutron.)

The symbol we use to represent nuclei is , where X represents the chemical symbol for the element. The subscript Z can be omited because the chemical symbol determine Z.

The nuclei of all atoms of a particular element must contain the same number of protons, but they may contain different numbers of neutrons. Nuclei that are related in this way are called isotopes. The isotopes of an element have the same Z value but different N and A values.

The proton carries a single positive charge, +e, where and the neutron is electrically neutral.

The masses of the proton and the neutron are almost equal,and about 2000 times as massive as the electron.

It is convinient to define the unified mass unit, u, in such a way that the mass of one atom of the isotope ¹²C is exactly 12u, where

XAZ

C 106.1 19−⋅=e

kg 1067.1 27−⋅

kg 1067.1 27−⋅=u

M. Dželalija, Physics (Part 21)CONTENTS Nuclear Stability

The very large repulsive electrostatic forcesbetween protons should cause the nucleus to fly apart. However, nuclei are stable, because of the presence of another, short-range force, the nuclear force. This is an attractive force that acts between all nuclear particles. The protons attract each other via the nuclear force, and at the same time they repel each other through the coulomb force. The nuclear force also acts between pairs of neutrons and between neutrons and protons.

The nuclear force dominates the coulomb force within the nucleus, and this strong nuclear force is nearly independent of charge.

2

M. Dželalija, Physics (Part 21)CONTENTS Nuclear Stability

There are about 260 stable nuclei; hundreds of others have been observed but are unstable. Light nuclei are most stable if they contain equal numbers of protons, but heavy nuclei are more stable if N>Z. Elements that contain more than 83 protons do not have stable nuclei.

M. Dželalija, Physics (Part 21)CONTENTS Binding Energy

The total mass of a nucleus is always less than the sum of the masses of its nucleons. Because mass is another manifestation of energy, the total energy of the bound system (the nucleus) is less than the combined energy of the separated nucleons. This difference in energy is called the binding energyof the nucleus and can be thought of as the energy that must be added to a nucleus to break it apart into its components. Therefore, in order to separate a nucleus into protons and neutrons, energy must be put into the system.

It is interesting to examine a plot of binding energy per nucleon E/A as a function of mass number for various stable nuclei. Nuclei with mass numbers greater or less than about 60 are not as strongly bound as those with about A=60.

3

M. Dželalija, Physics (Part 21)CONTENTS Radioactivity

In 1896 Becquerel accidentally discovered that uranium salt crystals emit an invisible radiation that can darken a photographic plateeven if the plate is covered to exclude light. This spontaneous emission of radiation was soon called radioactivity.

Three types of radiation can be emitted by a radioactive: alpha (α) rays, in which the emitted particles are He nuclei; beta (β) rays, in which the emitted particles are either electrons or positrons; and gamma (γ) rays, in which high-energy photons are emitted.

The three types of radiation have quite different penetrating powers, Alpha particles barely penetrate a sheet of paper, beta particles can penetrate a few milimeters of aluminium, and gamma rays can penetrate several centimeters of lead.

M. Dželalija, Physics (Part 21)CONTENTS Decay Constant

4

M. Dželalija, Physics (Part 21)CONTENTS Half-Life

M. Dželalija, Physics (Part 21)CONTENTS Alpha Decay

5

M. Dželalija, Physics (Part 21)CONTENTS Beta and Gamma Decays

M. Dželalija, Physics (Part 21)CONTENTS Carbon Dating

6

M. Dželalija, Physics (Part 21)CONTENTS Radiation Damage .

Radiation absorbed by matter can cause severe damage. The degree and type of damage depend on several factors, including the type and energy of the radiation and the properties of the absorbing material. Radiation damage in biological organisms is primarily due to ionization effects in cells. The normal function of a cell may be disrupted when highly reactive ions or radicals are formed as the result of ionizing radiation. Cells that do survive the radiation may become defective, which can lead to cancer.

In biological systems, it is common to separate radiation damage into two categories: somatic and genetic damage. Somatic damage is radiation damage to any cells except the reproductive cells. Such damage can lead to cancer at high radiation levels or seriously alter the characteristics of specific organisms. Genetic damage affects only reproductive cells. Damage to the genes in reproductive cells can lead to defective offspring.

Several units are used to quantify radiation exposure and dose. The rad (radiation absorbed dose) is defined as that amount of radiation that deposits 0.01 J of energy into 1 kg of absorbing material.

Although the rad is a perfectly good physical unit, it is not the best unit for measuring the degree of biological damage produced by radiation. This is because the degree of damage depends not only on the dose but also on the type of radiation. For example, a given dose of alpha particles causes about ten times more biological damage than equal dose of x-rays.

M. Dželalija, Physics (Part 21)CONTENTS Radiation Damage ..

The RBE (relative biological effectivness) factor is defined as the number of rad of x-radiation or gamma radiation that produces the same biological damage as 1 rad of the radiation being used.

The rem (roentgen equivalent in man) is defined as the product of the dose in rad and the RBE factor

(Dose in rem) = (dose in rad) x (RBE)According to this definition, q rem of any two radiation will produce the same

amount of biological damage. From table, we see that a dose of 1 rad of fast neutrons represents an effective dose of 10 rem and that 1 rad of x-radiation is equivalent to a dose of 1 rem.

Low-level radiation from natural sources, such as cosmic rays and radioactive rocks and soil, delivers to each of us a dose of about 0.13 rem/year. The upper limit of radiation dose (recommended) is 0.5 rem/year. An acute whole-body dose of 500 rem results in a mortality rate of about 50 %.

7


Can carbon-14 dating be used to measure the age of a stone?Carbon dating cannot generally be used to estimate the age of a stone, because the stone was not alive to take up carbon from the environment. Only the ages of artifacts that were alive can be estimated with carbon dating.

What fraction of a radioactive sample has decayed after two half-lives have elapsed?After the first half-life, half the original sample remains. After the second half-life a quarter of the original sample remains. Thus, three quarters of a radioactive sample has decayed after two half-lives.

A person whose mass is 75 kg is exposed to a whole-body dose of 25 rad. How many joules of energy are deposited in the person’s body?E = (75 kg)(25)(0.01 J/kg) = 18.75 J.

M. Dželalija, Physics (Part 21)CONTENTS Nuclear Fission

Nuclear fission occurswhen a heavy nucleus, such as U-235, splits, or fissions, into two smaller nuclei. In such a reaction, the total mass of the products is less than the original mass of the heavy nucleus.

A typical reactions of this type is

The fission fragments, barium and krypton, and the released neutrons have a great deal of kinetic energy following the fission event. Neutrons that are emitted can in turn trigger other nuclei to undergo fission, with the possibility of a chain reaction. If the chain reaction is not controlled, it could result in a violent explosion, with the release of an enormous amount of energy.

nn 10

9236

14156

23692

23592

10 3KrBaUU ++→→+

8

M. Dželalija, Physics (Part 21)CONTENTS Nuclear Reactor

The basic design of a nuclear reactor is shown in figure. The fuel elements consists of enriched uranium. Moderator substance regulate neutron energies slowing the neutrons down. Control rods are made of materials such as cadmium that are very efficient in absorbing neutrons. The rods controled the average number of neutrons from each fission event that will cause another event. This average number has to be 1.

M. Dželalija, Physics (Part 21)CONTENTS Nuclear Fusion

Binding energy for light nuclei is much smaller than the binding energy for heavier nuclei. When two light nuclei combine to form a heavier nucleus, the process is called nuclear fusion. Because the mass of the final nucleus is less than the masses of the original nuclei, there is a loss of mass accompanied by a release of energy. Although fusion power plants have not yet been developed, a great worldwide effort is under way to harness the energy from fusion reactions in the laboratory.

The hydrogen bomb, first exploded in 1952, is an example of an uncontrolled fusion.

All stars generate their energy through fusion processes. About 90 % of the stars, including the Sun, fuse hydrogen.The Sun radiates energy at the rate of 390 YW (yotta watt) and has been doing so for several billion years. The fusion in the Sun is a multistep process in which hydrogen is burned into helium. There is enough hydrogen to keep the Sun going for about 5 billion year into future.

Date post:	26-Nov-2015
Category:	Documents
Upload:	landato
View:	34 times
Download:	1 times

Physics

Documents